Some Approaches to Combining Probabilistic and Fuzzy Uncertainties
Abstract
Different types of uncertainty are widely spread in all areas of human activity. Probabilistic uncertainties are related to the chances of occurrence of random events. To deal with this kind of uncertainty, statistics and probability theory are successfully employed. Another kind of uncertainty, fuzzy uncertainties refer to imprecision and fuzziness of different kinds of measurements. To cope with this kind of uncertainty, the fuzzy set theory is used. This paper addresses widespread approaches to combining probabilistic and fuzzy uncertainties. The theoretical fundamentals of the approaches are considered within the context of the generalized theory of uncertainty (GTU).
Keywords: 
Fuzzy probability distribution; fuzzy uncertainty; fuzzy event; generalized constraint; probabilistic uncertainty; probability of fuzzy event; random variable

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